from the surface of Transparent Bodies. 



85 



from the formulae given by Fresnel and Brewster more than for 

 the other substances examined by M. Jamin. 



It remains for me now to explain the theoretical signification 

 of the alteration which I have proposed to make in Mr. Green's 

 formulae. In order to do so, it is necessary to give the equa- 

 tions from which he sets out, and to show where the restriction 

 occurs which prevents Mr. Green's formulae from accurately 

 representing the phenomena in their present state. 



In order to facilitate reference to Mr. Green's paper, I shall 

 retain his notation. 



Let x be perpendicular to the reflecting plane ; z and y lying 

 in this plane, and y in the plane of incidence. 



Let u, v denote the displacements parallel to x, y } the light 

 being polarized perpendicular to the plane of incidence. 



The conditions at the limits are (p. 17) — 



=sv, 



(4) 



du du t dv 

 dx dx dx 



combined with the understood condition, #=0 

 Let us assume 



dx dy ' 



dyjr 

 dy dx } 

 and transform equations (4). 



Mr. Green thus finds, referring to his equations (14) and (16), 







(5) 



dx 



<kb _ d(f) 

 dy 



d<f> dty __ dS, 

 dy dx dy 

 1 flftg _ 1 gfo 

 a* dt* ~ 



dx "*"" 



dy 

 dx 



(6) 



or dt* 



l_d?±_ ±<P± t 

 7 2 dt* ~ 7/ 2 df 



g, g t denoting the velocities of the normal wave in the two bodies 

 in contact ; y, y t the velocities of the transverse wave. 



Mr. Green substitutes in these equations, and in the general 

 equations of motion, the following expressions : — 



t/r=asin (ax + by + ct + e) +/3sm(—ax + by + ct + ej)~} 



<f> = e a ' x { A sin (by + ct) -f B cos (by + ct) } 

 tJt, = ot t sin (ape + by + ct) 

 <£ /= e -«/*{ A, sin (by + ct) + B, cos (by + ct) } 



h en 



